本次共计算 1 个题目:每一题对 x 求 1 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数(\frac{-1800sin(x)cos(x)}{(2{(2500 - 900({sin(x)}^{2}))}^{\frac{1}{2}})}) - 30sin(x) 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{-900sin(x)cos(x)}{(-900sin^{2}(x) + 2500)^{\frac{1}{2}}} - 30sin(x)\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{-900sin(x)cos(x)}{(-900sin^{2}(x) + 2500)^{\frac{1}{2}}} - 30sin(x)\right)}{dx}\\=&-900(\frac{\frac{-1}{2}(-900*2sin(x)cos(x) + 0)}{(-900sin^{2}(x) + 2500)^{\frac{3}{2}}})sin(x)cos(x) - \frac{900cos(x)cos(x)}{(-900sin^{2}(x) + 2500)^{\frac{1}{2}}} - \frac{900sin(x)*-sin(x)}{(-900sin^{2}(x) + 2500)^{\frac{1}{2}}} - 30cos(x)\\=&\frac{-810000sin^{2}(x)cos^{2}(x)}{(-900sin^{2}(x) + 2500)^{\frac{3}{2}}} - \frac{900cos^{2}(x)}{(-900sin^{2}(x) + 2500)^{\frac{1}{2}}} + \frac{900sin^{2}(x)}{(-900sin^{2}(x) + 2500)^{\frac{1}{2}}} - 30cos(x)\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!